Intuitively it has seemed to many that our concepts "conscious state" and "conscious creature" are sharp rather than vague, that they can have no borderline cases. On the other hand, many who take conscious states to be identical to, or realized by, complex physical states are committed to the vagueness of those concepts. In the paper I argue that "conscious state" and "conscious creature" are sharp by presenting four necessary conditions for conceiving borderline cases in general, and showing that some of those conditions cannot be met with "conscious state." I conclude that "conscious state" is sharp, and the conclusion is then extended to "conscious creature." The paper ends with a brief discussion of some implications